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3 years ago

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A researcher is using a regular, two-tailed test with α = .05 to determine whether a non-zero correlation exists in the populati

on. A sample of n = 25 individuals is obtained and produces a correlation of r = 0.21. The null hypothesis states that there is no correlation in the population. What is the t statistic, and what is the conclusion about the null hypothesis?
a. 1.03, the null hypothesis is rejected.

b. 1.03, the null hypothesis is not rejected.

c. 4.202, the null hypothesis is rejected.

d. 4.202, the null hypothesis is not rejected.

1 answer:

beks73 [17]3 years ago

7 0

Answer:

Step-by-step explanation:

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Read 2 more answers

Find thhe remainder when 7^203 is divided by 4

Aleksandr [31]

Using the square-and-multiply approach, we have

$7^{203}=7\times(7^{101})^2$
$7^{101}=7\times(7^{50})^2$
$7^{50}=(7^{25})^2$
$7^{25}=7\times(7^{12})^2$
$7^{12}=(7^6)^2$
$7^6=(7^3)^2$
$7^3=7\times7^2$

and so, using the property that, if $a_1\equiv b_1\mod n$ and $a_2\equiv b_2\mod n$ , then $a_1a_2\equiv b_1b_2\mod n$ , we get

$7\equiv3\mod4$
$7^2\equiv9\equiv1\mod4$
$7^3\equiv7\times1\equiv7\equiv3\mod4$
$7^6\equiv9\equiv1\mod4$
$7^{12}\equiv1\mod4$
$7^{25}\equiv7\times1\equiv7\equiv3\mod4$
$7^{50}\equiv9\equiv1\mod4$
$7^{101}\equiv7\times1\equiv7\equiv3\mod4$
$7^{203}\equiv7\times9\equiv3\times1\equiv3\mod4$

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3 years ago